Finite state bilaterally deterministic strongly mixing processes
Let \(\{X_n\}_{n\in\mathbb{Z}}\) be a two-sided sequence of i.i.d. random variables with finitely many states. The authors construct explicitly a factor sequence \(\{Z_n\}_{n\in\mathbb{Z}}\) of the above sequence that has finitely many states, and is \(\alpha\)-mixing and bilaterally deterministic, i.e. each of the \(Z_n\)'s is measurable w.r.t. the double-tail \(\sigma\)-field generated by \(\{Z_n\}_{n\in\mathbb{Z}}\). This result complements an earlier example by \textit{R. C. Bradley} [Trans. Am. Math. Soc. 294, 233-241 (1986; Zbl 0595.60040)] of a \(\rho\)-mixing, bilaterally deterministic process with continuous state space.
scientific article; zbMATH DE number 952560